RHeology of INertial particles by means of experimental Observations and numerical Simulations
Table of contents
Jointly funded by the German Research Foundation (DFG) and the French National Research Agency (ANR).
Project Description
The RHINOS group at TU Dresden combines experiments and particle-resolved simulations to investigate dense, particle-laden suspensions across the visco-inertial transition. By varying the fluid viscosity, shear rate, particle pressure, and particle-particle friction, changes in volume fraction, stress transfer, hydrodynamic forces, and contact networks can be demonstrated over a wide range of Stokes numbers. As part of the measurement campaign, laminar, pressure-driven shear flows over idealized sediment beds are also being investigated. These high-resolution data bridge the gap between experiments and numerical modeling, elucidate mechanisms missing from the constitutive equations developed for the respective limit cases, and support improved two-phase models for engineered and natural particle-laden flows, including sediment transport.
The Science: From Viscous to Inertial
The Problem
Dense suspensions occur in sediment transport, industrial processes, and geophysical flows, yet their behavior between the viscous and inertial limits remains inadequately described. At low Stokes’ numbers, the fluid’s viscosity and lubrication dominate stress transfer; at high Stokes’ numbers, particle inertia and frictional contacts become decisive. Existing constitutive laws are generally calibrated for one of the two limits and do not consistently capture the transition. Experiments also show that the particle volume fraction and macroscopic friction do not change at the same rate, suggesting different transitions in granular pressure and shear stress. RHINOS is therefore investigating which mechanisms at the particle level govern this transition and how they should be represented in predictive models.
Rolling vs. Sliding Contacts
The Stokes number $St$ indicates the ratio of particle inertial stresses to viscous stresses. Particle-resolved simulations localize the transition in granular pressure at $St \approx 8$, close to the experimental value $St \approx 10$. The shear stress changes more slowly. This discrepancy is attributable to the interaction of tangential contact, lubrication, and long-range hydrodynamic forces. In viscosity-dominated flows, strong, long-lasting rolling contacts form coherent networks. As inertia increases, the network becomes more fluidized, and sliding contacts predominate. Their onset depends not only on St but also on the distance to jamming. Increasing particle-particle friction delays the transition of shear stress to higher Stokes numbers.
Tangentialkraftnetzwerke trennen sich in überwiegend rollende Kontakte im viskosen Bereich und gleitende Kontakte im Trägheitsbereich.
Our Method
RHINOS combines controlled rheological experiments with grain-resolved simulations and micromechanical analyses.
Pressure-Induced Rheometry
Spheres with neutral buoyancy are sheared between roughened plates under controlled granule pressure. By varying the fluid viscosity and shear rate, the transition from viscous to inertial behavior is covered, while simultaneous measurements of packing fraction and macroscopic friction distinguish the pressure response from the shear stress response
Druckauferlegte Geometrie © TPH
Particle-Resolved Simulations
In the three-dimensional simulations, an immersed boundary method for flow is combined with a discrete element method for particle contacts. These simulations account for near-field lubrication, far-field hydrodynamics, normal contact forces, and tangential friction. The numerical cell replicates the geometry experimentally defined by pressure and investigates Stokes numbers in the range of approximately 0.01 to 300.
Micromechanical Analysis
Macroscopic friction is decomposed into hydrodynamic, normal, and tangential contact components. By visualizing the force network, rolling and sliding contacts are then separated, and the sliding component is quantified. By scaling this component based on the distance to failure, the data can be summarized across different viscosities, thereby linking local contact rearrangements to volume-averaged rheology.
Der gleitende Anteil kollabiert über die Viskositäten, wenn die Stokes-Zahl durch die Entfernung zum Blockieren skaliert wird
Model Integration
The identified relationships between the Stokes number, grain pressure, packing fraction, and shear stress are implemented as constitutive terms in two-phase flow models. This links grain-scale micromechanics with macroscopic predictions of sediment transport under pressure-driven flow.
Project Objectives
- To investigate the transition between particle pressure and shear stress in the visco-inertial regime.
- Determining the extent to which rolling and sliding contacts, hydrodynamic lubrication, particle-particle friction, and the distance to the stagnation point influence the rheology of suspensions.
- Provision of reference data and improved constitutive equations for two-phase models of sediment transport and particle-laden flow
Project Team Funding
Project Leaders
Prof. Dr.-Ing. Bernhard Vowinckel (DFG) and Prof. Pascale Aussillous (ANR)
Scientific coordination and supervision of the experimental, numerical, rheological, and sediment transport-related components of the project.
Senior Research Associates
- Dr. Sudarshan Konidena
- Dr. Franco Tapia
- Prof. Dr. Élisabeth Guazzelli
Principal investigators responsible for field campaigns, particle-resolved simulations, the implementation of methods, quantitative data analysis, and the micromechanical interpretation of the rheology of dense suspensions.
Funding Agencies
The German Research Foundation (DFG) and the French National Research Agency (ANR) as part of the joint ANR-DFG funding projects VO2413/3-1 and ANR-21-CE30-0050.
Host Institution
Scientific Basis and Source of the Figure
S. Konidena et al., “Tangential Forces Govern the Viscous-Inertial Transition in Dense Frictional Suspensions,” Physical Review Letters 136, 248201 (2026)